Math Intervention 3–5 Grade

90 Addition and Subtraction Concepts

What is the Partial Differences Concept?

The partial differences concept is a subtraction strategy that

involves combining differences into workable clusters. Like

partial sums, this concept is an alternative to the traditional

algorithm. Instead of following rules that are meaningless to

some students, students using the partial differences strategy do

not have to align columns, start with the ones, or cross out. Instead,

they fi nd the difference between the tens, then fi nd the difference

between the ones, and combine these differences. For example,

57 – 26 = (50 – 20) + (7 – 6). Here, the difference between the tens

is 30 and the difference between the ones is +1. These partial

differences combine to 30 + 1 = 31. The partial differences concept

is also an effective strategy when a subtraction situation involves

decomposing. For example, 84 – 36 = (80 – 30) + (4 – 6). Here,

the difference between the tens is 50 and the difference between

the ones is –2. These partial differences combine to 50 – 2 = 48.

CCSS

Operations and Algebraic Thinking

Number and Operations in Base Ten

Formative Assessment

To fi nd out if a student understands partial differences, ask

the student to solve the following equations:

37 – 12 = 45 – 23 = 57 – 34 =

64 – 25 = 52 – 36 = 70 – 28 =

Ask the student to explain how she solves each problem.

Invite the student to try the problems without aligning

the digits in columns, without starting with the ones, and

without crossing out.

Partial Differences

CONCEPT: